Problem: Solve for $x$ and $y$ using substitution. ${x+y = -1}$ ${y = -6x-11}$
Solution: Since $y$ has already been solved for, substitute $-6x-11$ for $y$ in the first equation. ${x + }{(-6x-11)}{= -1}$ Simplify and solve for $x$ $x-6x - 11 = -1$ $-5x-11 = -1$ $-5x-11{+11} = -1{+11}$ $-5x = 10$ $\dfrac{-5x}{{-5}} = \dfrac{10}{{-5}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = -6x-11}\thinspace$ to find $y$ ${y = -6}{(-2)}{ - 11}$ $y = 12 - 11$ $y = 1$ You can also plug ${x = -2}$ into $\thinspace {x+y = -1}\thinspace$ and get the same answer for $y$ : ${(-2)}{ + y = -1}$ ${y = 1}$